In this circuit, we are asked to analyze the current through $R_2$ when capacitor $C_2$ is fully charged. Let's go through the reasoning step-by-step.

1. Capacitor Behavior: When a capacitor is fully charged, it behaves like an open circuit because no further current can flow through it. Hence, once $C_2$ is fully charged, the branch containing $R_2$ and $C_2$ will have no current flowing through it.

2. Current through $R_2$: Since $C_2$ is fully charged, no current will flow through the $R_2$ branch, making the current through $R_2$ zero.

Thus, the correct answer to the question is:

• The current is zero.

Would you like further clarification or details? Here are some related questions to deepen your understanding:

1. How does the charging time of a capacitor depend on its capacitance and resistance?
2. What happens to the total current $I_0$ in the circuit once $C_2$ is fully charged?
3. How can we determine the voltage across $R_1$ after $C_2$ is fully charged?
4. What is the role of $C_1$ in this circuit configuration?
5. What changes occur in the circuit if $C_2$ were replaced with a resistor?

Tip: When analyzing circuits with capacitors, remember that capacitors block DC current after becoming fully charged, which can simplify the analysis.